Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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ON MEDIAL Q-ALGEBRAS

  • Received : 2009.10.16
  • Published : 2010.07.31
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Abstract

In this paper, we show that the mapping ${\varphi}(x)\;=\;0*x$ is an endomorphism of a Q-algebra X, which induces a congruence relation "~" such that X/$\varphi$ is a medial Q-algebra. We also study some decompositions of ideals in Q-algebras and obtain equivalent conditions for closed ideals. Moreover, we show that if I is an ideal of a Q-algebra X, then $I^g$ is an ignorable ideal of X.

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References

  1. S. S. Ahn and H. S. Kim, On QS-algebras, J. Chungcheong Math. Soc. 12 (1999), 33–41.
  2. Q. P. Hu and X. Li, On BCH-algebras, Math. Sem. Notes Kobe Univ. 11 (1983), no. 2, part 2, 313–320.
  3. Q. P. Hu and X. Li, On proper BCH-algebras, Math. Japon. 30 (1985), no. 4, 659–661.
  4. K. Iseki, On BCI-algebras, Math. Sem. Notes Kobe Univ. 8 (1980), no. 1, 125–130.
  5. K. Iseki and S. Tanaka, An introduction to the theory of BCK-algebras, Math. Japon. 23 (1978/79), no. 1, 1–26.
  6. Y. B. Jun, E. H. Roh, and H. S. Kim, On BH-algebras, Sci. Math. 1 (1998), no. 3, 347–354
  7. J. Neggers, S. S. Ahn, and H. S. Kim, On Q-algebras, Int. J. Math. Math. Sci. 27 (2001), no. 12, 749–757. https://doi.org/10.1155/S0161171201006627
  8. J. Neggers and H. S. Kim, On d-algebras, Math. Slovaca 49 (1999), no. 1, 19–26.